Geometrical instrument



May 9, 1933 o. w. RICHARDS ET AL v 1,907,873

GEOMETRICAL INSTRUMENT l Filed March 2, 1952 OSCAR w. RICHARDS PERCY M. ROOPE lNvl-:NToRs `ATTORNEY APatented May 9, 1933 UNITED STAT-Es laafrailw'I-f OFFICE OSCAR W. RICHARDS, F NEW HAVEN, CONNECTICUT, AND PEBCY M. ROOPE, O

WORCESTER,

MASSACHUSETTS GEOMETRICAL INSTRUMENT Application led March 2, 1932. Serial No. 598,312.

-This invention relates to geometrical instruments and more particularly it has reference to a device which can be used Ifor directly measuring the tangent to a curve .at

any point or for precisely locating and drawing a tangent to a curve at any point.

One ofthe objects of our invention is to provide an improved device for directly measuring the tangent to a curve at any point and indicating the angle whichthe tangent makes with an axis. Another ohject is to provide an improved device for laying out and drawing a tangent to a curve. 'A further object is to provide means for accurately measuring and determining'the slope of a line whichis tangent to aA curve at any-point. These and other objects and i ladvantages reside in certain novel features of construction, arrangement and combination of parts as will hereinafter be more fully described and pointed out in the lappendedclaims.'

Referring to the drawing:

Fig. 1 is a top plan of a ing our invention.l

Fig. 2 is a vertical, central section of same.

Figs. 3, 4 and 5 illustrate the operation and use of our device. v

One embodiment of our Ainvention is il-l lustrated in the drawing wherein 10 indicates a base plate which is preferably formed of a transparent material such as any of the well known cellulosic or other transparent materials. The base 10 has a central opening 11 withinwhich is ixedly mounted-a metal bearing ring 12.- -:Rotatably mounted on the ring 12 is a mounting 13 to which a transparent glass plate 14 is fixedly secured. Positioned on top of base 10 is acircular metal plate 15 which is secured to therotatable mountingv 13 by means of three screws 16 so that the mounting 13 is held against the bearing 12 and the circular plate 15 is free to rotate together with the' glass plate 14.

Ruled, etched or otherwiseapplied to glass plate 14 are the two-ducial lines 17 and 18 which are at: 'right angles to each other. A triangular glass prism 19 is fixedly mounted on the top of glass plate 14 by device embodycementing with Canada balsam, for enample. The prism 19 may have an isoscles or equilateral form and it is so mounted that its apex edge 2O is parallel with iiducial line 17. Mounted on base A10 is a Vernier plate 55 24 having a Vernier which cooperates `with a circular scale 23, engraved on plate 15, for

-indicating the anglar position, in degrees,

of plate 15.

An inderl plate 21, secured to base .10,

to indicate the value of the tangent, as will hereinafter be described. The transparent base 10 is also provided Withthe two reference lines 26 and 27 for indicating the a: and 65 y axes, respectively. The glass plate 14 is provided wlth two small apertures 28, shown in exaggerated size on the drawing for clearness. These two apertures are, located 'in alignment along the fiducial line 18 for 70 a urpose to be hereinafter described.

he operation of our device will now be described with reference to Figs. 3, 4.and 5. Withthe plate 15 positioned as in Fig. 1, an observer looking down from above the prism 75 Will see, due to therefractive `effect of the prism, two images 17 and 17 of iiducial line 17, equally spaced from the vertical plane of the apex edge'20 of the prism, as shown in Fig.'3. Assuming lnow that it is 80 desired to determine the value of a tangent to a curve C at a given point P, the device is placed on the sheet, bearing the curve, so that the oint of intersection of line 18 and images 1 and 17 is positioned above the 3 5 point P on the curve. The device is positioned so that line 26 is parallel to the w-axis of the graph. An observer u on looking down upon the prism will then, or example, see the images 17 and 1 and the two dis- 90 placed branches C and C" of the curve C, as shown in Fig'. 4. The plate 15 together with prism 19 is then rotated by means of the rojecting screws 16, until the two brano es C and C are brought together to form a continuous curve when viewed through the prism, as shown in Fig.'5. By means of the index line 22, Athe value of the tangent, or slope, at the point P is then read directly from scale 25. The angle which 100 has an index line 22 which coop- 60 'crates with the tangent scale 25 on plate 15 the tangent makes with the .a1-axis is indicated in degrees by scale 23 and cooperating Vernier 24. As shown on Fig. 1, the scales 23 and 25 are arranged to indicate the angles and tangents Whether negative or positive.

If it is desired to actually draw a line which is tangent to the curve at point P, the settings are made as above outlined and then the tangent is locatedby marking the graph with a pin through the two apertures 28. The device is removed and the tangent is then drawn by connecting the two pin holes in the paper with a straight line. This provides a very accurate method for laying out and drawing a tangent t a curve.

From the foregoing, it is apparent that we are able to attain the objects of our in- Curve.

vention and provide an improved device for directly measuring the tangent to a curve, determining the angle which a tangent makes with an axis and accurately locating and drawing a tangent to a curve. Although we have described a device having a transparent base plate and a metal scale plate, it is obvious that any suitable materials could be used. For example, both base and scale plate could be made of a transparent material. Our device provides a very rapid method for determinin the tangent and also an accurate means for ocating and drawing a tangent to a curve. Since a break in the continuity of a curve can be readily detected, the setting of the prism of our device is quite sensitive. It has been proposed to use reflecting rules for locating and drawing tangents and normals to curves. Such rules are based on the principle that a curve passes into its reflection without a bend, if the mirror is placed exactly at right angles to the curve. Small curves, or those which alternate considerably in their curvature cannot however, be determined with sufiicient accuracy as the minor bends are diflicult to recognize. Our device, however, provides rapid and accurate means for determining, locating and drawing tangents to Our instrument is of considerable use to those doing graphical work involving rates of change, especially in case the equation of the curve to be differentiated is unknown. Thus, a biologist can use the instrument fr determining the rate of growth of an organism, at any time, from the ,growth Engineers, physicists and others who deal with experimental, empirical or statistical matters will also find our device useful and convenient. For example, a transparent plate having fiducial lines and locating apertures can be surmounted by a fixed prism and used for accurately locating and drawing tangents to curves. Such, and other modifications of our invention will obviously occur to those skilled in the art.

We claim:

1. A device of the type described comprising a base, a glass plate mounted on said base, a triangular prism fixedly mounted on said plate, two mutually perpendicular fiducial lines beneath said prism, the apex edge of said prism being substantially parallel with one of said lines.

2. A device of the type described comprising a transparent plate having two perpendicular fiducial marks, a triangular prism mounted on said plate with one of its faces in contact with said plate, the apex edge of said prism being substantially parallel to one of said fiducial marks.

3. An instrument of the type described comprising a plate having a sight opening, a triangular prism mounted above said o ening, means defining two perpendicular ines in fixed relation to .and beneath said prism, the apex edge of said prism being parallel to one of the lines of said means.

4. An instrulnent of the type described comprising a transparent plate having means defining two fiducial lines at right angles to each other, optical means fixedly mounted on said plate for producing two laterally spaced'images of one of said lines,

said plate havingtwo spaced apertures, said apertures being positioned along the other of said lines.

5. A device of the type described comprising a base having means defining two fiducial lines at right angles to each other, a glass plate mounted on said base, said plate having means defining two fiducial lines at right angles to each other and a triangular prism mounted on said plate one of its faces in 'contact with said plate, the apex edge of said prism being substantially parallel with one of said lines on said plate.

6. An instrument of the type described comprising la base, a member rotatably mounted on said base, a triangular prism mounted on said member, two mutually perpendicular indicating lines beneath said prism, the apex of said prism being substantially parallel to one of said lines and scale means for indicating the angular position of said member.

7. An instrument of the type described cpmprising a base having an opening, a member rotatably mounted on said base, said member having a centrally dis osed transparent plate bearing crossed fi ucial marks, a triangular prism mounted on said plate, the apex edge of said prism lying in the vertical plane of one of said marks, said plate having apertures positioned in alignment with the other of said marks.

8.v An instrument of the t pe described comprising a base, a memllier rotatably mounted on said base, said member having two iiducial lines at right angles to each other, a triangular prism mounted on said nooners member above said lines, the apex edge of the prism being parallel to one of said lines and scale means associated with said member for indicating the slope of the other of said lines. l

9. An instrument of the type described com rising a base, an a erture member rof tata ly mounted on sai base, a transparent plate mounted on said member, a triangular 1 prism secured to said late with one of its faces in contact with t e late, two iiducial devices positioned at rig t angles to each other beneath said prism,one of said fiducial devices lying in the plane of the apex edge of said prism, and scale means for in- `Llcating the angular position of said mem- Vr. 10.' A device of the type described comprising la triangular prism, a fiducial mark .beneath one face of said prism, said mark being positioned in the vertical plane of the upper apex ledge of said prism and`means for rotating said prism about said mark.

11.` In a device of the type described a tri- 'angular prism, fiducial line means beneath one face of said prism, said means being in fixed relation to said-prism, said prism hav-l ing an apex edge opposite said face, said means comprising means defining a line 30 which is parallel to said edge and means delining another line which is perpendicular to and intersects said first named line below said apex edge.,-

12. A device of the type described comprising a' member havin-g means defining two mutually perpendicular lines, a trian gular prismv mounted above said member and in fixed relation thereto, the point ofintersection of said' lines being positioned in 1.40 thev vertical plane of the apex 'edge of the rism. p 13. A device of the type described comprising a base havingan opening, a member rotatably mounted in said opening, a transparent plate carried by said member, said plate having two mutually perpendlcular fducial lines, a triangular Vprism iixedly mounted on said plate, the point of intersection of said lines being positioned in the vertical plane of the a x edge of said prism, scale means for in icating the angles which one-of said lines make with an axis andother scale means for indicating the tangents of the repective angles.

OS AR W. RICHARDS. PERCYM. ROOPE. .y 

